There are several button combinations that can be used to instantly unlock some of the features of the game.
Unlock all Puzzles in Puzzle University
Unlock Very Hard difficulty setting
Unlock Super Hard difficulty setting
Game speed over 50 in marathon mode
Unlock All Trainers
Play as Mewtwo
At the trainer select screen, hold on controller 1 and press , , , , , , , , , or complete the game under the Super Hard difficulty setting. Note that Player 2 will always be Mewtwo, while Player 1 is always Ash.